Recent content by LogarithmLuke

So this is the correct scheme? ##-4\frac{\mu}{h^2} U_{i,j}+(\frac{v_{1}}{2 h}+\frac{\mu}{h^2})U_{i+1,j}+(\frac{v_{2}}{2 h} +\frac{\mu}{h^2})U_{i,j+1} - (\frac{v_{1}}{2 h}-\frac{\mu}{h^2})U_{i-1,j} - (\frac{v_{2}}{2 h} - \frac{\mu}{h^2})U_{i,j-1} + \tau = f_{ij}## How would I transition further...

Im not familiar with what the diffusion terms and advection terms of the equation are. I did not think about whether the velocity components were independent of x and y, I simply dotted the components with the nabla vector for u, where I replaced the partial derivatives with central differences.

Yes this is a 2D problem. The last ##U_N## should have been a ##U_S##. Ok so using subscript indicies i and j instead I obtain the following scheme: ##4\frac{\mu}{h^2} U_{i,j}+(\frac{v_{1}}{2 h}-\frac{\mu}{h^2})U_{i+1,j}+(\frac{v_{2}}{2 h} -\frac{\mu}{h^2})U_{i,j+1} - (\frac{v_{1}}{2...

So for my scheme I obtained ##\frac{\mu}{h^2} U_{p}+(\frac{v_{1}}{2 h}-\frac{\mu}{h^2})U_{E}+(\frac{v_{2}}{2 h} - \frac{\mu}{h^2})U_{N} - (\frac{v_{1}}{2 h}+\frac{\mu}{h^2})U_{W} - (\frac{v_{2}}{2 h} + \frac{\mu}{h^2})U_{N} + \tau = f## however I am not sure this is correct. I am quite new to...

Homework Statement: Use Taylor expansion to show that for ##u \in C^4([0,1]) ## $$ max |\partial^+\partial^-u(x) - u''(x)| = \mathcal{O}(h^2)$$ For ##x \in [0,1]## and where the second order derivative ##u''## can be approximated by the central difference operator defined by...

My apologies. So i calculated that the long-run mean fraction of time a single individual has a cold is ##7/107## so i figured ##7/107## or about ##0.065## of the population will be infected in the long term. Does the calculation seem correct?

So if the birth rate is $$\lambda(n-i)$$ and we know that approx 0.065 of the population are infected. So our arrival rate becomes $$ \lambda(5.26*10^6 - 0.065*5.26*10^6)*0.01$$ since only 1% of arrivals require hospitalization. This gives $$W = \approx 4 days$$ which seems like a reasonable answer?

The reason i proposed $$\frac{\lambda}{i}$$is because the birth rate becomes lower as more people get infected. But with that reasoning $$\lambda * (n-i)$$for the birth rate, and $$\mu i$$ for the death rate as you propose also makes sense. Yes I have sketched the jump chain, the states can...

Assume that an individual only has two possible states: susceptible (S) and infected (I). Further, assume that the individuals in the population are independent, and that for each susceptible individual the time until the next infection follows an exponential distribution with expected value 1/λ...

I understand it a lot better now, thank you. Was it true that two of the three vectors forming a tetrahedron can be in the same plane, though?

The cross product of vectors AB and AC must be perpendicular to both AB and AC. So does that mean vector AD is also perpendicular to AB and AC as its perpendicular to the cross product between them? Or is it that the only way for vector AD to be perpendicular to the cross product of vectors AB...

Hi, I am having trouble understanding why three vectors that lie in the same plane can't form a tetrahedron. If the plane is somewhat vertical or titlted will it not be possible for one vector to higher up than another so that you have a difference in height? Also, for three vectors to form a...

Im aware of what the magnetic fields around the wires look like, the trouble comes with finding the direction of the forces between to conductors.

Hi, I am having trouble figuring out how the forces work between two straight conductors with currents going through them. I know that when the currents go the same way, the forces are attractive, and when the currents go opposite ways, the forces are repelling. I know one has to use the right...

Why isn't it constant when the speed is constant and the rate of change in area is constant? The problem doesent specify, but based on the answers section were supposed to find the average and max values for each of the positions. However, positions 1,3 and 5 all have emf values of 0 (why is...